Exponential Groups 2: Extensions of Centralizers and Tensor Completion of CSA-Groups

This is the second article in the series of papers by the authors on the theory of exponential groups. In the first one [15] we discussed foundations of this theory. Definitions necessary for independent understanding of the present article are given in the introduction and the first section. The theory of exponential groups begins with results of A.Mal'cev [11], P.Hall [7], G.Baumslag [4] and R.Lyndon [9]. The axiomatic notion of an exponential group was introduced by R.Lyndon (1960). In [13] a new axiom was added to Lyndon's definition to obtain a new notion of an exponential group. The refined version is more convenient because it coincides exactly with the notion of a module over a ring in the abelian case, whereas abelian exponential groups after Lyndon provide a far wider class. Recall the main definition from [13]. Let A be an arbitrary associative ring with identity and G a group.